If you decide to send a message to the nearest star (or a possible planet around this star) how long would it take to arrive if you used green light? How long would it take if you sent a signal in the radio with the Arecibo Radio Telescope?
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The speed of electromagnetic wave in a vacuum is a constant and doesn't depend on its wavelength. So the answers for green light and for radio signal are the same.
The closest star (besides our sun) is called Proxima Centauri, and the distance to it is 4.2 light years (see the link). By the definition of a light year, light (or any electromagnetic wave) goes through it during one year.
So the time after which our signal will arrive is 4.2 years (approximately).
(also, the distance between stars and their planets, and the distance waves will travel through atmospheres are negligible).
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